Simplify the following expression: $\dfrac{22a^3}{12a^3}$ You can assume $a \neq 0$.
Answer: $ \dfrac{22a^3}{12a^3} = \dfrac{22}{12} \cdot \dfrac{a^3}{a^3} $ To simplify $\frac{22}{12}$ , find the greatest common factor (GCD) of $22$ and $12$ $22 = 2 \cdot 11$ $12 = 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(22, 12) = 2 $ $ \dfrac{22}{12} \cdot \dfrac{a^3}{a^3} = \dfrac{2 \cdot 11}{2 \cdot 6} \cdot \dfrac{a^3}{a^3} $ $\phantom{ \dfrac{22}{12} \cdot \dfrac{3}{3}} = \dfrac{11}{6} \cdot \dfrac{a^3}{a^3} $ $ \dfrac{a^3}{a^3} = \dfrac{a \cdot a \cdot a}{a \cdot a \cdot a} = 1 $ $ \dfrac{11}{6} \cdot 1 = \dfrac{11}{6} $